| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 18 |
| Paper | Download PDF ↗ |
| Topic | Hypothesis test of binomial distributions |
| Type | Multiple binomial probability calculations |
| Difficulty | Standard +0.3 This is a straightforward S1 hypothesis testing question with standard binomial calculations. Parts (i)-(iii) are routine probability calculations using B(15, 1/6). Part (iv) requires setting up one-tailed tests and comparing probabilities to 10% significance level—standard textbook procedure. Part (v) asks for basic interpretation. All steps are mechanical with no novel insight required, making it slightly easier than average. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities2.05a Hypothesis testing language: null, alternative, p-value, significance2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail |
2 A game requires 15 identical ordinary dice to be thrown in each turn.\\
Assuming the dice to be fair, find the following probabilities for any given turn.
\begin{enumerate}[label=(\roman*)]
\item No sixes are thrown.
\item Exactly four sixes are thrown.
\item More than three sixes are thrown.
David and Esme are two players who are not convinced that the dice are fair. David believes that the dice are biased against sixes, while Esme believes the dice to be biased in favour of sixes.
In his next turn, David throws no sixes. In her next turn, Esme throws 5 sixes.
\item Writing down your hypotheses carefully in each case, decide whether\\
(A) David's turn provides sufficient evidence at the $10 \%$ level that the dice are biased against sixes.\\
(B) Esme's turn provides sufficient evidence at the $10 \%$ level that the dice are biased in favour of sixes.
\item Comment on your conclusions from part (iv).
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 Q2 [18]}}